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Solving integrals/ dy/(2*y+1)

Integral of dy/(2*y+1) dy

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1           
  /           
 |            
 |     1      
 |  ------- dy
 |  2*y + 1   
 |            
/             
0
$$\int\limits_{0}^{1} \frac{1}{2 y + 1}\, dy$$ 
Integral(1/(2*y + 1), (y, 0, 1))
Detail solution

  1. Let .

    Then let and substitute :

    1. The integral of a constant times a function is the constant times the integral of the function:

      1. The integral of is .

      So, the result is:

    Now substitute back in:

  2. Now simplify:

  3. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                             
 |                              
 |    1             log(2*y + 1)
 | ------- dy = C + ------------
 | 2*y + 1               2      
 |                              
/
$$\int \frac{1}{2 y + 1}\, dy = C + \frac{\log{\left(2 y + 1 \right)}}{2}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
log(3)
------
  2
$$\frac{\log{\left(3 \right)}}{2}$$ 
=
= 
log(3)
------
  2
$$\frac{\log{\left(3 \right)}}{2}$$ 
log(3)/2
Numerical answer [src] 
0.549306144334055
0.549306144334055

    Use the examples entering the upper and lower limits of integration.

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